Batting Average in Batter vs. Pitcher Battle Verlander throws fastball Verlander throws curveball Betts guesses fastball .260 .240 Betts guesses curveball .180 .350 What’s the Nash equilibrium? It can be solved with a little algebra—and as you’ve probably guessed, it involves randomization. It turns out that Verlander should throw the fastball about 58 percent of the time and Betts should guess fastball about 89 percent of the time. With this mix, Betts hits for a .252 average. That’s better than he could do with a “pure strategy” where he always picked the same move.
